An Active Lattice Model in a Bayesian Framework

A Markov Random Field is used as a structural model of a deformable rectangular lattice. When used as a template prior in a Bayesian framework this model is powerful for making inferences about lattice structures in images. The model assigns maximum probability to the perfect regular lattice by penalizing deviations in alignment and lattice node distance. The Markov random field represents prior knowledge about the lattice structure, and through an observation model that incorporates the visual appearance of the nodes, we can simulate realizations from the posterior distribution. A maximum a posteriori (MAP) estimate, found by simulated annealing, is used as the reconstructed lattice. The model was developed as a central part of an algorithm for automatic analysis of genetic experiments, positioned in a lattice structure by a robot. The algorithm has been successfully applied to many images, and it seems to be a fast, accurate, and robust solution to the problem. Several possible extensions of the model are described.